Exponential inequalities for Bessel processes
Extending the Wong-Zakai theorem to reversible Markov processes
We show how to construct a canonical choice of stochastic area for paths of reversible Markov processes satisfying a weak Hölder condition, and hence demonstrate that the sample paths of such processes are rough paths in the sense of Lyons. We further prove that certain polygonal approximations to these paths and their areas converge in -variation norm. As a corollary of this result and standard properties of rough paths, we are able to provide a significant generalization of the classical result...
Feller semigroups and degenerate elliptic operators with Wentzell boundary conditions
This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with Wentzell boundary conditions in the characteristic case. Our results may be stated as follows: We can construct Feller semigroups corresponding to a diffusion phenomenon including absorption, reflection, viscosity, diffusion along the boundary and jump at each point of the boundary.
Fernique type inequalities and moduli of continuity for l2-valued Ornstein-Uhlenbeck Processes
Filtrage de diffusions bidirectionnelles pour une observation ponctuelle de Poisson à deux paramètres
First eigenvalue of one-dimensional diffusion processes.
First hitting time of the boundary of the Weyl chamber by radial Dunkl processes.
First order calculus and last entrance times
Fonctionnelles additives de diffusions et de processus de branchement
Formule de Taylor stochastique et développement asymptotique d'intégrales de Feynman
Fractional flux and non-normal diffusion.
Further exponential generalization of Pitman's theorem.
G-convergence of generators and weak convergence of diffusions
General approximation method for the distribution of Markov processes conditioned not to be killed
We consider a strong Markov process with killing and prove an approximation method for the distribution of the process conditioned not to be killed when it is observed. The method is based on a Fleming−Viot type particle system with rebirths, whose particles evolve as independent copies of the original strong Markov process and jump onto each others instead of being killed. Our only assumption is that the number of rebirths of the Fleming−Viot type system doesn’t explode in finite time almost surely...
Generalised transforms, quasi-diffusions, and Désiré André's equation
Generalized Bessel function of type .
Geometric evolution under isotropic stochastic flow.
Grossissement d'une filtration et retournement du temps d'une diffusion
Harmonic analysis on fractal spaces
Harmonic functions along Brownan balls an the Liouville property for solvable Lie groups.